Let $f:[-1,1] \rightarrow R$ be defined as $f(x)=a x^2+b x+c$ for all $x \in[-1,1]$ where $a, b, c \in R$ such that $f(-1)=2, f^{\prime}(-1)=1$ and for $x \in(-1,1)$ the maximum value of $f^{\prime \prime}(x)$ is $\frac{1}{2}$. If $f(x) \leq \alpha, x \in[-1,1]$, then the least value of $\alpha$ is equal to $\_\_\_\_$ .